HessenbergQ

[stevengj]

It might be a good idea to use or emulate the HessenbergQ type from LinearAlgebra: this is a type to encode all of the Householder reflectors, and provides specialized methods to multiply vectors and matrices by Q or Q', as well as a Matrix conversion to get the ordinary matrix (which would replace your getQ function).

Ideally, you could just use the HessenbergQ object as-is, as long as you encode your householder reflectors in the same way. (This also allows you to use LAPACK routines to multiply by the reflectors.)

[smataigne]

I adapted the Hessenberg type so that it admits a Tridiagonal matrix as reduced matrix. The type returned by hessenberg(A) is now a standard Hessenberg type.